In a recently published short note, F. K. Levin (1989) discusses the relation between the "moveout velocities" of P-P, P-SV, and SV-SV reflections from the bottom of a transversely isotropic layer with a vertical symmetry axis. We refer to such a medium as one exhibiting "polar anisotropy." Levin's note was prompted by a paper of Tessmer and Behle (1988), and it is relevant to a paper by Iverson and others (1989), both of which discuss the computation of shear velocities from moveout velocities obtained with P-P and P-S reflections. Levin's note addresses the practically important question of the use of this method in the presence of polar anisotropy, a phenomenon which we believe occurs almost universally in the sedimentary layers of the real earth. Levin suggests that polar anisotropy of "typical" magnitude must be considered in this problem. He uses as an estimate of typical magnitudes data given by Thomsen (1986) and concludes from numerical examples that the method of estimating shear velocities proposed by Tessmer and Behle and by Iverson may be subject to unacceptably large errors in many real cases. Moreover, Levin suggests that the source of these errors is mysterious.